The classical homeschooling style takes an approach used beginning in the time of ancient Greece and Rome: teaching the Trivium. The Trivium is the "five tools of learning," which include reason, record, research, relate and rhetoric. Classical homeschool curriculum focuses not only on the traditional subjects, but also incorporates a strong focus on grammar, logic and rhetoric.
The school-at-home style of homeschooling involves teaching a boxed curriculum. With this style, each student typically has his own textbooks. While you decide lesson plans, learning milestones and tests revolve around the curriculum. According to the Homeschool website, this method of education is the most expensive.
The Waldorf method, also used in traditional schools, was developed in the early 1900s by Rudolf Steiner. It emphasizes educating not only the mind, but the body and spirit of the student. The Waldorf method focuses on the three phases of child development --- imitation, imagination and discrimination or judgment. Rather than learning out of a traditional textbook, students learn by participating in arts and crafts, which help develop imagination, and by pursuing learning in areas they find most interesting rather than following strict curriculum guidelines.
The Montessori style, also used in traditional education, encourages students to learn at their own pace. The method focuses on the differences of each child, recognizing that education is not a one-size-fits-all approach. Children 6 and younger are put into small groups to explore a variety of age-appropriate activities in a safe environment. Older children plan their own activities, such as projects and field trips, without the use of a textbook or structured schedule. Montessori also emphasizes cleanliness and neatness, preferring uncluttered work spaces.
Unschooling is the most liberal method of homeschooling, as it allows students to completely pursue their own interests in each subject. According to the Homeschool website, John Holt, the founder of this movement, claims that since children have been learning their entire lives, the traditional method of education actually disrupts the natural inclination to learn. An environment using this method would have no structure or schedule. No textbooks or materials are offered to students, and there are no exams to take.